So, now the above integral can be solved by using integral by parts, try doing it!

P.S: Here,[tex]u=\sqrt{x^2+1} [/tex] and v=1.

Ok, so after an integration by parts, now you have to integrate x^2/sqrt(x^2+1). How is that a simplification? I think you are doing the parts integration wrong. You need to have u=sqrt(x^2+1) and v=x.